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It is rated "Very hard". He's usually able to solve them, but he was having a bit of trouble today. He asked me for help but I couldn't add what he had already written.

My dad's attempt: enter image description here

Online recreation for easier solving: enter image description here

I tried using Sudoku calculators and they solved it accurately but without providing the justification for any number. I sometimes couldn't understand some of the deductions.

I'd appreciate an answer that provides some information and reasoning on how to proceed further, with 1 or 2 useful number marked to pave the way :).

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  • $\begingroup$ Would you be able to embed those images into the question itself, rather than linking to them externally? $\endgroup$ Commented Dec 22, 2024 at 12:25
  • $\begingroup$ The site told me to link them. I can embed them though, sure. $\endgroup$ Commented Dec 22, 2024 at 12:27
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    $\begingroup$ Please cite where this sudoku is from. For example, if it's a newspaper puzzle, the name of the paper and the specific issue $\endgroup$ Commented Dec 22, 2024 at 15:27

2 Answers 2

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There's a

1-6 pair in box 4.

This can be utilised by considering the square r6c8: whether it's a 3 or a 5 (the only options), in box 4 it must be somewhere on the middle row.

This puts that square's contents on the top row in box 5, and since it must be a 3 or a 5, it can only go in the empty square.

This places the 4 in box 5 and gets us started.

enter image description here

For the next step,

pencil marking the other-coloured 3-5 in box 5, we notice that r5c7 sees both colours (that is, both a 3 and a 5, in one order or the other) and is therefore a naked single 7,

after which the puzzle gives up without any further resistance.

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We shall use the chess notation to refer to the board. There is a key cell.

It is h4, which is 3 or 5.

Suppose first that h4 is 5. Then b4 is 9, i5 is 9, a3 is 9, b3 is 5, a5 is 5, d6 is 5, d5 is 4, e5 is 3, d1 is 3, f1 is 5, e8 is 5, f8 is 3, c8 is 9, a8 is 4, a4 is 7, c4 is 4, and there remains no number for c5. 

 271 946 .8.
 489 153 276
 635 782 194

 8.2 597 ...
 5.. 438 ..9
 794 261 85.

 957 814 6..
 348 629 ...
 126 375 948

So h4 is 3. Then c5 is 3, d6 is 3, f1 is 3, d1 is 5, e5 is 5, d5 is 4, f8 is 5, e8 is 3, g6 is 4, g9 is 3, i9 is 5, i3 is 3, h3 is 2, i5 is 3, i4 is 9, i2 is 7, i6 is 1, h2 is 1, g2 is 5, g5 is 7, h6 is 5, h5 is 6, b5 is 1, a5 is 9, c8 is 9, a8 is 4, b6 is 6, c4 is 4, a4 is 7, b4 is 5, a3 is 5, and b3 is 9. 

 271 946 385
 489 135 276
 635 782 194

 862 397 451
 913 458 762
 754 261 839

 597 814 623
 348 629 517
 126 573 948

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  • $\begingroup$ This method is called bifurcation, which is a brute-force method, and thus often deemed unsavoury. $\endgroup$ Commented Dec 22, 2024 at 21:32
  • $\begingroup$ @Bass rot13(Gur pnyphyngvbaf jrer rnfl naq fubeg, naq V bsgra fcrag zber gvzr gb fbyir n fhqbxh. Ohg gur erny yhpx jnf gb thrff gur xrl pryy, juvpu fgnegrq gur punva ernpgvbaf yrnqvat gb n pbagenqvpgvba be n fbyhgvba). $\endgroup$ Commented Dec 22, 2024 at 21:44

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